7n^2+8n=12

Solution for 7n^2+8n=12 equation:

Simplifying
7n2 + 8n = 12

Reorder the terms:
8n + 7n2 = 12

Solving
8n + 7n2 = 12

Solving for variable 'n'.

Reorder the terms:
-12 + 8n + 7n2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + 8n + 7n2 = 0

Factor a trinomial.
(-2 + -1n)(6 + -7n) = 0

Subproblem 1
Set the factor '(-2 + -1n)' equal to zero and attempt to solve:

Simplifying
-2 + -1n = 0

Solving
-2 + -1n = 0

Move all terms containing n to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + -1n = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1n = 0 + 2
-1n = 0 + 2

Combine like terms: 0 + 2 = 2
-1n = 2

Divide each side by '-1'.
n = -2

Simplifying
n = -2
Subproblem 2
Set the factor '(6 + -7n)' equal to zero and attempt to solve:

Simplifying
6 + -7n = 0

Solving
6 + -7n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -7n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7n = 0 + -6
-7n = 0 + -6

Combine like terms: 0 + -6 = -6
-7n = -6

Divide each side by '-7'.
n = 0.8571428571

Simplifying
n = 0.8571428571
Solution
n = {-2, 0.8571428571}